v^2/64=16.5

Solution for v^2/64=16.5 equation:

v^2/64=16.5

We move all terms to the left:

v^2/64-(16.5)=0

We add all the numbers together, and all the variables

v^2/64-16.5=0

We multiply all the terms by the denominator


v^2-(16.5)*64=0

We add all the numbers together, and all the variables

v^2-1056=0

a = 1; b = 0; c = -1056;
Δ = b2-4ac
Δ = 02-4·1·(-1056)
Δ = 4224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4224}=\sqrt{64*66}=\sqrt{64}*\sqrt{66}=8\sqrt{66}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{66}}{2*1}=\frac{0-8\sqrt{66}}{2}
=-\frac{8\sqrt{66}}{2}
=-4\sqrt{66}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{66}}{2*1}=\frac{0+8\sqrt{66}}{2}
=\frac{8\sqrt{66}}{2}
=4\sqrt{66}
$